A generalization of Anderson’s theorem on unimodal functions
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- by Somesh Das Gupta PDF
- Proc. Amer. Math. Soc. 60 (1976), 85-91 Request permission
Abstract:
Anderson (1955) gave a definition of a unimodal function on ${R^n}$ and obtained an inequality for integrals of a symmetric unimodal function over translates of a symmetric convex set. Anderson’s assumptions, especially the role of unimodality, are critically examined and generalizations of his inequality are obtained in different directions. It is shown that a marginal function of a unimodal function (even if it is symmetric) need not be unimodal.References
- T. W. Anderson, The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities, Proc. Amer. Math. Soc. 6 (1955), 170–176. MR 69229, DOI 10.1090/S0002-9939-1955-0069229-1
- Govind S. Mudholkar, The integral of an invariant unimodal function over an invariant convex set—an inequality and applications, Proc. Amer. Math. Soc. 17 (1966), 1327–1333. MR 207928, DOI 10.1090/S0002-9939-1966-0207928-6
- S. Sherman, A theorem on convex sets with applications, Ann. Math. Statist. 26 (1955), 763–767. MR 74845, DOI 10.1214/aoms/1177728435
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 85-91
- MSC: Primary 26A87; Secondary 52A40
- DOI: https://doi.org/10.1090/S0002-9939-1976-0425050-7
- MathSciNet review: 0425050